## Early Papers on Interval Computations

### Origins of Interval Computations: from Archimedes to 1960s

Achimedes used two-sided bounds to compute Pi:
Archimedes, "On the measurement of the
circle", In: Thomas L. Heath
(ed.), *The Works of Archimedes*, Cambridge University Press,
Cambridge, 1897; Dover edition, 1953, pp. 91-98.

The concept of a function having values which are bounded within
limits was discussed by W. H. Young:
W. H. Young, "Sull due funzioni a piu valori constituite dai limiti
d'una funzione di variable reale a destra ed a sinistra di ciascun
punto", *Rendiconti Academia di Lincei, Classes di Scienza Fiziche*,
1908, Vol. 17, No. 5, pp. 582-587.

The concept of operations with a set of multi-valued numbers was
introduced by R. C. Young, who developed a formal algebra of
multi-valued numbers:
The special case of closed intervals was further developed by P. S. Dwyer:
Interval mathematics was further developed by
M. Warmus:
by T. Sunaga:
and by R.
E. Moore
For an early history of interval computations, see also

S. Markov and K. Okumura, "The Contribution of T. Sunaga to
Interval Analysis and Reliable Computing", In: T. Csendes (ed.),
*Developements in Reliable Computing*, Kluwer, Dordrecht,
1999, pp. 167-188.

### Selected Papers from the 1970s and 1980s

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